Chip-to-chip communications are frequently used in telecommunication devices. The speed of the interfaces for such telecommunication devices can exceed 25 Gbps to transmit or receive data. Also, such interfaces are used in a wide range of applications such as peripheral component interconnect (“PCI”) express serial links and double data rate (“DDR”) memory input/output (“I/O”) links. By increasing the data rate of transceivers, the signal bandwidth is impacted by the capacitive loads at the front end of the receiver.
To mitigate the signal loss, equalizers are used in transmitter and receiver side of a transceiver. By increasing the data rate to 25 Gbps or more, the use of coils is inevitable. One of the main capacitive loads is due to electrostatic discharge (“ESD”) protection devices. Usually, two types of ESDs are present in every transceiver application, e.g., one for a human body model (“HBM”), which can reach about 2000V, and another for charged device model (“CDM”), which can reach about 500V. The capacitance for these ESDs can be about 400 fF.
Additionally, there are other capacitance sources in a receiver such as metal lines, active devices, and on-die termination (“ODT”) resistance. In particular, the ODT resistance has a considerable large capacitance, usually more than 100 fF. Since there is no way to physically reduce or altogether remove those capacitive loads, one method is to electrically hide them and/or contribute those capacitive loads.
FIG. 1 illustrates a prior art transceiver system using t-coils for contributing capacitive loads. In the prior art transceiver system, the transceiver system can be implemented for a differential pair of signals DIP and DIN such that for each one of the differential pair of signals there is a transmitter side, a channel, and a receiver side. The transceiver system comprises transmitters 18a and 18b, resistors 20a-20b, t-coils 22a-22b, ESDs 24a-24b, transmitter pads 26a-26b, printed circuit board (“PCB”) channels 28a-28b, receiver pads 30a-30b, t-coils 32a-32b, ESDs 34a-34b that can be implemented by capacitors having a capacitance CESD, on-die termination (“ODT”) 38a-38b each having a capacitance Cr and a resistance Rterm, and receivers 40a-40b. Each of the t-coils 22a-22b and 32a-32b comprise two serially connected inductors.
The transmitter 18a drives the signal DIP through the coupled resistor 20a, t-coil 22a, and the ESD 24a to the transmitter pad 26a. The transmitted signal can then be received at the receiver pad 30a via the channel 28a. From there, the received signal travels through the coupled t-coil 32a, the ESD 34a, and the ODT 38a to the receiver 40a for output as a received signal RXP.
Likewise for the signal DIN, the transmitter 18b drives the signal DIN through the coupled resistor 20b, t-coil 22b and the ESD 24b to the transmitter pad 26b. The transmitted signal can then be received at the receiver pad 30b via the channel 28b. From there, the received signal travels through the coupled t-coil 32b, the ESD 34b, and the ODT 38b to the receiver 40b for output as a received signal RXN.
The t-coil network used in both transmitter side and the receiver side can improve return loss and insertion loss. For each side of the transceiver, the t-coil network can provide for an impedance matching circuit. In using a conventional t-coil, the main capacitive loads are coupled to the t-coil between the serially connected inductors of the t-coil.
For instance, the ESD 24a has one end coupled to the serial connection between the inductors La and Lb of the t-coil 22a. The ESD 24b has one end coupled to the serial connection between the inductors La and Lb of the t-coil 22b. Likewise on the receiver side, the ESD 34a has one end coupled to the serial connection between the inductors L1 and L2 of the t-coil 32a. The ESD 34b has one end coupled to the serial connection between the inductors L1 and L2 of the t-coil 32b. 
FIG. 2 illustrates an equivalent circuit diagram for a t-coil used in the receiver side of the prior art transceiver system. The receiver side of the prior art transceiver system illustrated in FIG. 1 can be modeled by the circuit diagram illustrated in FIG. 2. Referring to FIG. 2, a classic t-coil network consists of two coupled inductors L1m and L2m that have a mutual inductance M with a coupling factor K. The mutual inductance M can be modeled by having a third inductor LM coupled to the t-coil. The simplified t-coil after applying an effect of mutual inductance is:L1m=L1−Lm  EQ[1]L2m=L2−Lm  EQ[2]Lm=−K√{square root over (L1L2)}  EQ[3]
A t-coil network can be used in a front end of a receiver with various ODT placements. The ODT can be a variable resistor having resistance Rterm (e.g., 50 ohm) to set channel impedance and can also have a high capacitance CR.
The ODT is placed at one end of t-coil network to hide the effectiveness of the ODT capacitance CR from an input terminal IN of the t-coil. Thereby input return loss is improved because the CESD capacitance is the primary impedance at the input terminal of the t-coil network. However, while this technique improves input return loss, it increases input capacitive load on the input stage of the receiver.
FIG. 3 illustrates another prior art transceiver system using t-coils for contributing capacitive loads. There can be different methods to contribute the capacitive loads of the ESD and the ODT. In such alternative configuration, to mitigate input capacitive loads on the input stage of the receiver, the ODT 38a is disposed in parallel with the ESD 34a with one end of the parallel connection coupled to a middle serial connection of the t-coil network 32a, and the ODT 38b is disposed in parallel with the ESD 34b with one end of the parallel connection coupled to a middle serial connection of the t-coil network 32b. The drawback in such alternative configuration is an increase of capacitance at the input terminal of the t-coil networks 32a and 32b, which degrades the return loss.
FIG. 4 illustrates an equivalent circuit diagram for another configuration of a t-coil used on the receiver side of the prior art transceiver system illustrated in FIG. 3. In this equivalent circuit, a t-coil comprises two inductors, where the two inductors L1M and L2M are serially connected across an input and an output. An effective capacitance across the input and the output can be represented by the capacitor Cp for modeling purposes. The middle point of the t-coil (i.e., the serial connection between the L1M and L2M) is further coupled to an end of an inductor LM, where the inductor LM is used for modeling of the mutual inductance and is not an actual physical component. Another end of the inductor LM is coupled to the capacitors CESD and CR and resistors Rterm. The drawback here is that the total capacitance (i.e., CESD+CR) is increased, which results in degrading the return loss.
FIG. 5 illustrates a generic t-coil of the prior art coupled to a receiver side. In essence, the t-coil can be described by the following equations for finding insertion loss and return loss.
                    M        =                  K          ⁢                                                    L                1                            ⁢                              L                2                                                                        EQ        ⁡                  [          4          ]                                                  V          1                =                                            [                              Z                11                            ]                        ⁢                          I              1                                +                                    [                              Z                12                            ]                        ⁢                          I              2                                                          EQ        ⁡                  [          5          ]                                                  V          2                =                                            [                              Z                21                            ]                        ⁢                          I              1                                +                                    [                              Z                22                            ]                        ⁢                          I              2                                                          EQ        ⁡                  [          6          ]                                                  Z          11                =                              1            +                                          L                1                            ⁢                              Cs                2                                              Cs                                    EQ        ⁡                  [          7          ]                                                  Z          12                =                              Z            21                    =                                    1              -                              MCs                2                                      Cs                                              EQ        ⁡                  [          8          ]                                                  Z          22                =                              1            +                                          L                2                            ⁢                              Cs                2                                              Cs                                    EQ        ⁡                  [          9          ]                    
With s=jω, then:
                              Z          11                =                              1            -                                          L                1                            ⁢              C              ⁢                                                          ⁢                              ω                2                                                          jC            ⁢                                                  ⁢            ω                                              EQ        ⁡                  [          10          ]                                                  Z          12                =                              Z            21                    =                                    1              +                              MC                ⁢                                                                  ⁢                                  ω                  2                                                                    jC              ⁢                                                          ⁢              ω                                                          EQ        ⁡                  [          11          ]                                                  Z          22                =                              1            -                                          L                2                            ⁢              C              ⁢                                                          ⁢                              ω                2                                                          jC            ⁢                                                  ⁢            ω                                              EQ        ⁡                  [          12          ]                    
The insertion loss S21 can be written as follows:
                    Insertion        ⁢                                  ⁢        loss        ⁢                  :                ⁢                                  ⁢        20        ⁢                  log          ⁡                      (                          S              21                        )                                              EQ        ⁡                  [          13          ]                                                  S          21                =                  2          ×                                                    Z                21                            ⁢                              Z                O                                                                                      (                                                            Z                      11                                        +                                          Z                      O                                                        )                                ⁢                                  (                                                            Z                      22                                        +                                          Z                      O                                                        )                                            -                                                Z                  12                                ⁢                                  Z                  21                                                                                        EQ        ⁡                  [          14          ]                    where Zo is direct current (“DC”) resistance, which can be about 50 ohm due to the termination resistance Rterm. The Equation [14] shows that factor Z12 (since Z12=Z21) is a main factor to determine insertion loss. In fact, it determines the real part of denominator. For example, the denominator (“Denom”) can be as follows:
                    Denom        =                                                            (                                                      Z                    11                                    +                                      Z                    O                                                  )                            ⁢                              (                                                      Z                    22                                    +                                      Z                    O                                                  )                                      -                                          Z                12                            ⁢                              Z                21                                              =                                                    (                                                                            1                      -                                                                        L                          1                                                ⁢                        C                        ⁢                                                                                                  ⁢                                                  ω                          2                                                                                                            jC                      ⁢                                                                                          ⁢                      ω                                                        +                                      Z                    O                                                  )                            ⁢                              (                                                                            1                      -                                                                        L                          2                                                ⁢                        C                        ⁢                                                                                                  ⁢                                                  ω                          2                                                                                                            jC                      ⁢                                                                                          ⁢                      ω                                                        +                                      Z                    O                                                  )                                      +                                          (                                                      1                    +                                          MC                      ⁢                                                                                          ⁢                                              ω                        2                                                                                                  C                    ⁢                                                                                  ⁢                    ω                                                  )                            2                                                          EQ        ⁡                  [          15          ]                    
The main factor of S21 is
                                          1                          C              ⁢                                                          ⁢              ω                                +                      M            ⁢                                                  ⁢            ω                          =                              1                          C              ⁢                                                          ⁢              ω                                +                      ω            ⁢                                                  ⁢            K            ⁢                                                            L                  1                                ⁢                                  L                  2                                                                                        EQ        ⁡                  [          16          ]                    
When capacitance C increases, the denominator of S21 reduces resulting in increased insertion loss. Additionally, to optimize IL of coil, input inductance L1 should be smaller than output inductance (L2>L1).
Alternating current (“AC”) gain can be extracted from the insertion loss. If input and output loading is equal, then the AC gain can be written as the following:
                              AC          ⁢                                          ⁢          gain          ⁢                      :                    ⁢                                          ⁢                                    V              2                                      V              1                                      =                              S            21                    2                                    EQ        ⁡                  [          17          ]                    
In fact, the factor S21 is changing over frequency. In the t-coil structure, by increasing frequency, the insertion loss will be degraded since the denominator of S21 is increased, resulting in reducing S21 and consequently the AC gain.
The return loss S11 can be written as follows:
                    Return        ⁢                                  ⁢        loss        ⁢                  :                ⁢                                  ⁢        20        ⁢                  log          ⁡                      (                          S              11                        )                                              EQ        ⁡                  [          18          ]                                                  S          11                =                                                            (                                                      Z                    11                                    -                                      Z                    O                                                  )                            ⁢                              (                                                      Z                    22                                    +                                      Z                    O                                                  )                                      -                                          Z                12                            ⁢                              Z                21                                                                                        (                                                      Z                    11                                    +                                      Z                    O                                                  )                            ⁢                              (                                                      Z                    22                                    +                                      Z                    O                                                  )                                      -                                          Z                12                            ⁢                              Z                21                                                                        EQ        ⁡                  [          19          ]                                                  Z          11                =                              1            -                                          L                1                            ⁢              C              ⁢                                                          ⁢                              ω                2                                                          jC            ⁢                                                  ⁢            ω                                              EQ        ⁡                  [          20          ]                                                  Z          12                =                              Z            21                    =                                    1              +                              MC                ⁢                                                                  ⁢                                  ω                  2                                                                    jC              ⁢                                                          ⁢              ω                                                          EQ        ⁡                  [          21          ]                                                  Z          22                =                              1            -                                          L                2                            ⁢              C              ⁢                                                          ⁢                              ω                2                                                          jC            ⁢                                                  ⁢            ω                                              EQ        ⁡                  [          22          ]                    When Z21=Z12,
                              S          11                =                                                            (                                                      Z                    11                                    -                                      Z                    O                                                  )                            ⁢                              (                                                      Z                    22                                    +                                      Z                    O                                                  )                                      -                                          (                                  Z                  12                                )                            2                                                                          (                                                      Z                    11                                    +                                      Z                    O                                                  )                            ⁢                              (                                                      Z                    22                                    +                                      Z                    O                                                  )                                      -                                          (                                  Z                  12                                )                            2                                                          EQ        ⁡                  [          23          ]                    the factor S11 is determined by Z11 as a main parameter.
                              Z          11                =                                            1              -                                                L                  1                                ⁢                C                ⁢                                                                  ⁢                                  ω                  2                                                                    jC              ⁢                                                          ⁢              ω                                =                      -                          j              ⁡                              (                                                      1                                          C                      ⁢                                                                                          ⁢                      ω                                                        -                                                            L                      1                                        ⁢                    ω                                                  )                                                                        EQ        ⁡                  [          24          ]                    
From equation, Z11 depends on capacitance and input inductance L1. If it is assumed L1=L2, Z11 equals Z22, then
                              S          11                =                                                            (                                  Z                  11                                )                            2                        -                                          (                                  Z                  O                                )                                            2                ⁢                                                                  -                                                      (                                          Z                      12                                        )                                    2                                                                                                        (                                  Z                  11                                )                            2                        +                          2              ⁢                              Z                11                            ⁢                              Z                O                                      +                                          (                                  Z                  O                                )                            2                        -                                          (                                  Z                  12                                )                            2                                                          EQ        ⁡                  [          25          ]                                                  S          11                =                                            -                                                (                                                            1                                              C                        ⁢                                                                                                  ⁢                        ω                                                              -                                                                  L                        1                                            ⁢                      ω                                                        )                                2                                      -                                          (                                  Z                  O                                )                            2                        +                                          (                                                      1                                          C                      ⁢                                                                                          ⁢                      ω                                                        +                                      M                    ⁢                                                                                  ⁢                    ω                                                  )                            2                                                                                                                -                                                                  (                                                                              1                                                          C                              ⁢                                                                                                                          ⁢                              ω                                                                                -                                                                                    L                              1                                                        ⁢                            ω                                                                          )                                            2                                                        -                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          (                                                                        1                                                      C                            ⁢                                                                                                                  ⁢                            ω                                                                          -                                                                              L                            1                                                    ⁢                          ω                                                                    )                                        ⁢                                          Z                      O                                                        +                                                                                                                                                (                                              Z                        O                                            )                                        2                                    +                                                            (                                                                        1                                                      C                            ⁢                                                                                                                  ⁢                            ω                                                                          +                                                  M                          ⁢                                                                                                          ⁢                          ω                                                                    )                                        2                                                                                                          EQ        ⁡                  [          26          ]                    
From reflection coefficient S11, the increase of capacitance C improves return loss in the low frequency, but by increasing frequency, the increase of capacitance results in degrading return loss, shown in FIG. 10. When capacitance C increases, the denominator of S21 reduces, resulting in an increase of the insertion loss.
Therefore, it is desirable to provide improved new methods, systems, and circuits for mitigating return loss and insertion loss for a receiver of a high-speed transmission.